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Sinuous antennas can provide ultra-broadband operation, frequency-independent embedding impedances and isolated dual polarizations, making them suitable for many applications in the terahertz frequency regime. In this paper, a lens-coupled planar sinuous antenna has been designed and fabricated for terahertz balanced mixers. Simulation results show that the antenna exhibits a nearly frequency-independent embedding impedance of ~100 Ω over a broad frequency range. To verify the aforementioned antenna properties at THz frequencies, a Schottky diode was mounted to the center of the antenna to realize a direct detector. The radiation patterns of the lens-coupled sinuous antenna were studied at 196 GHz and 585 GHz. A responsivity of 300-1000 V/W was measured up to 900 GHz demonstrating the ultra-broadband operation of the antenna. In addition, an isolation of larger than 15 dB between the two polarizations has been demonstrated for both the frequency ranges of 190-210 GHz and 570-630 GHz.